Chemical Physics Letters 471 (2009) 85–91
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Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett
Broadband dielectric response of dichloromethane
Johannes Hunger a, Alexander Stoppa a, Andreas Thoman b, Markus Walther b, Richard Buchner a,*
a
b
Institut für Physikalische und Theoretische Chemie, Universität Regensburg, D-93040 Regensburg, Germany
Department of Molecular and Optical Physics, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany
a r t i c l e
i n f o
Article history:
Received 17 December 2008
In final form 10 February 2009
Available online 13 February 2009
a b s t r a c t
A systematic study of the dielectric response of dichloromethane over a broad frequency range
(8:5 6 m=GHz 6 1000; 6 4:3 THz at 25 °C) at temperatures from 5 to 35 °C is reported. The spectra are
best described by a superposition of three contributions. The dominating loss peak at 70 GHz, fitted
by a modified Debye equation accounting for inertial rise, represents the rotational diffusion of molecular
dipoles. Additionally, two libration modes contribute, which are described by damped harmonic oscillators of resonance frequencies 0:9 THz and 2:1 THz. While the latter modes reflect the anisotropy of
the dichloromethane molecule, the diffusive reorientation at long times appears to be rather isotropic.
Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction
Due to its low boiling point (40 °C [1]), high density
3
(1:3266 kg dm [1]) and its immiscibility with hydrogen-bonding
solvents like water, dichloromethane (DCM, CH2 Cl2 , Fig. 1) is
widely used as a solvent in synthetic chemistry and technical
applications, especially for separation processes [2]. Being a small
molecule with the same C2v symmetry and similar gas-phase
dipole moment as water (DCM: l ¼ 1:61 D [3]; H2 O: 1.85 D [1])
but without the ability to form H-bonds, the structure and dynamics of liquid DCM received considerable attention in the 1980s,
when it was selected by the European Molecular Liquids Group
as one of the target compounds for a collaborative project on the
consistent evaluation of molecular dynamics in liquids [4].
At that time the far-infrared absorption spectrum of pure DCM
[5,6] and its mixtures [3] were studied in some detail in the
30—200 cm1 region, albeit with the limited accuracy then accessible. The aim was to gain information on intermolecular vibration
and libration motions and to test interaction potentials for computer simulations [7]. However, only a small number of studies
[8–10] explored the adjoining microwave to mm-wave frequencies
because this region at 70 GHz, where the main dielectric dispersion occurs [8], was and to some extent still remains difficult to access. To our knowledge the present investigation is the first study
that addresses the temperature dependence of the dielectric spectrum of DCM in the GHz to THz region.
Due to its sensitivity to all kinds of dipole fluctuations dielectric
spectroscopy (DS) is an efficient tool to study the dynamics and
interaction in liquids [11,12]. Like conventional (far-)infrared spectroscopy DS probes the total polarization, ~
PðtÞ, of a sample in a
* Corresponding author. Fax: +49 941 943 4532.
E-mail address: Richard.Buchner@chemie.uni-regensburg.de (R. Buchner).
0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2009.02.024
time-dependent field, ~
EðtÞ, albeit at lower frequencies and thus
longer timescales. In DS this response is conventionally expressed
in terms of the complex permittivity spectrum, ^eðmÞ ¼ e0 ðmÞ ie00 ðmÞ.
The relative permittivity e0 ðmÞ shows a dispersion from the static
permittivity, e, to the high-frequency limit e1 . The dielectric loss,
e00 ðmÞ, expresses the energy dissipation which arises from the coupling of ~
EðtÞ to dipole fluctuations.
In this Letter, we report the dielectric spectra of DCM in the
temperature range of 5–35 °C, covering the frequency range of
8:5 6 m=GHz 6 1000 ð0:28—33cm1 Þ. At 25 °C the spectrum was
extended up to 4:3 THz ð144 cm1 Þ by including literature data
[5]. A thorough investigation of DCM dynamics appears to be
timely because in contrast to previous assumptions [7] recent simulations and cluster calculations showed the importance of the
quadrupole moment for the interactions in liquid DCM [13] and
indicated a strong contribution of induced dipoles to the far-infrared spectrum [14]. Additionally, existing information on the
dynamics of DCM obtained with dielectric/far-infrared [5,6], NMR
[15], and Raman [16] spectroscopies is somewhat conflicting. As
will be shown below the present data resolve most of these discrepancies and should thus help to improve the existing potential
models. Last but not least the proper characterization of ^eðmÞ for
pure DCM is worthwhile because DCM solutions receive increasing
attention in dielectric studies [17–20] and DCM appears to be a
suitable standard for the calibration of certain dielectric spectrometers [21].
2. Experimental
Dichloromethane was obtained from Acros Organics, Belgium
(analytical grade, >99.99%) and stored over freshly activated
molecular sieve (3 Å). Coulometric Karl–Fischer titration yielded
a water content of <5 ppm for the investigated sample. Although
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J. Hunger et al. / Chemical Physics Letters 471 (2009) 85–91
tails, like optical path length, were given). The refractive index was
then calculated for the region 1:2 6 m=THz 6 4:3 ð40—144 cm1 Þ
by numerical integration of Eq. (1) with the trapezoidal method.
The anchor value for the refractive index, n1 , was adjusted for best
Þ in 1.2–2.3 THz
overlap of experimental and calculated nðm
ð40—77 cm1 Þ. The obtained ^eðmÞ spectrum is displayed in Fig. 3;
Fig. 4 shows the corresponding spectra of refractive index and
absorption coefficient.
For the formal description of ^eðmÞ various relaxation models
based on sums of up to four individual contributions to the spectrum were tested with a non-linear least-squares routine which
simultaneously fits e0 ðmÞ and e00 ðmÞ [27,28]. The quality of the fit
was evaluated by the reduced error function v2r
v2r ¼
Fig. 1. Dichloromethane with its axes of inertia. Moments of inertia for rotation
around x, y and z are Ix ¼ 2:62 1047 kg m2 ; Iy ¼ 25:26 1047 kg m2 , and
Iz ¼ 27:37 1047 kg m2 [8]. The dipole moment of magnitude l ¼ 1:61 D [3] is
parallel to the z-axis.
"
#
N
N
X
X
1
we0 ðmi Þde0 ðmi Þ2 þ
we00 ðmi Þde00 ðmi Þ2
2N m 1 i¼1
i¼1
ð4Þ
where de0 ðmi Þ and de00 ðmi Þ are the residuals, N is the number of data
triples ðmi ; e0 ðmi Þ; e00 ðmi ÞÞ, and m the number of the adjustable parameters. Experimental data were weighted statistically (we00 ðmi Þ ¼
je00 ðmi Þ1 j and we0 ðmi Þ ¼ je0 ðmi Þ1 j) to give the values of e0 and e00 equal
importance in the simultaneous fit with Eqs. (5) and (6).
3. Results and discussion
the concentration of 1-pentene, added as a stabilizer to DCM by the
manufacturer, was below the detection limit samples were kept at
35 °C for at least 3 h prior to measurements to avoid evaporation of
the stabilizer during data collection.
Complex permittivity spectra, ^eðmÞ, were determined in the
frequency range of 8:5 6 m=GHz 6 1000 by combining data obtained with four waveguide interferometers (IFM) [22] at
8:5 6 m=GHz 6 89 and a transmission THz-time-domain spectrometer (THz-TDS) [23] covering 0:117 6 m=THz K 1:0. Except for the
X-band IFM (8.5–12 GHz), operating only in the temperature range
of 15 6 #= C 6 35, all instruments cover 5 6 #= C 6 35 with an
accuracy of 0:05 C for the IFM and 1 C for the THz-TDS. None
of these instruments requires calibration with a dielectric standard. As can be seen from Fig. 2 there is a seamless fit of the data
points obtained with the various instruments, indicating the absence of systematic errors in ^eðmÞ.
At 25 °C the frequency range could be extended to 2 THz with a
THz-TDS in reflection geometry [24]. Additionally, far-infrared
absorption coefficients, a, covering 1.2–4.3 THz ð40—144 cm1 Þ,
were taken from Vij et al. [5] and converted to ^eðmÞ with the help
of the Kramers–Kronig (KK) relation [25]
i Þ n1 ¼
nðm
1
2p2
Z
0
1
aðmÞ dm
2
m m2i
ð1Þ
and the equations
a 2
e0 ¼ n2 4p m
na
00
e ¼ 2pm
ð2Þ
ð3Þ
Þ, and the absorption coefficient,
relating the refractive index, nðm
aðmÞ, at wavenumber m ¼ m=c0 to the corresponding permittivity,
e0 ðmÞ, and loss, e00 ðmÞ; c0 is the speed of light in vacuo [26].
Þ and e00 ðm
Þ deterFor the KK transformation the data for e0 ðm
Þ.
Þ and aðm
mined in our laboratory were first converted into nðm
The resulting absorption coefficients were combined with the
aðmÞ values extracted from the digitized far-infrared spectrum of
Ref. [5] at 298 K (their Fig. 1). To match both sets of data in the
Þ values
overlapping region of 1.2–2.3 THz ð40—77 cm1 Þ the aðm
from the literature had to be multiplied by 1.1. This might be
due to errors in the digitization of the graph, as well as due to inaccuracies of the far-infrared spectra themselves (no instrument de-
3.1. Dichloromethane at 25 °C
In accordance with previous literature [8,9], at high frequencies,
m > 100 GHz, the dielectric spectra of DCM (Figs. 2 and 3) deviate
considerably from the shape expected for simple exponential
relaxation, indicating the onset of molecular librations. Evaluation
of the various fit models tested for the 25 °C spectra (Fig. 3) indeed
revealed the presence of three modes: the main dispersion step
centered at 70 GHz and two high-frequency modes peaking at
0:4 THz and 1:8 THz in the ^eðmÞ representation (corresponding
to the shoulder at 0:9 THz ð 30 cm1 Þ and the peak at
2:3 THz ð 77 cm1 Þ in aðmÞ, Fig. 4).
Two libration modes could be expected from the symmetry of
CH2 Cl2 . Therefore, the high-frequency contributions were both
modeled as damped harmonic oscillators (DHOs) with resonance
frequencies, mi ði ¼ 2; 3Þ, and damping constants, ci . For the feature
at 70 GHz associated with DCM relaxation a symmetrically
broadened Cole–Cole equation was suggested [8], albeit with a
very small width parameter of aCC ¼ 0:03. For the present spectra
:
a Debye equation ðD; aCC ¼ 0Þ is sufficient to model ^eðmÞ at low frequencies. However, correction for the inertial rise of dipole reorientation is required to avoid unphysical far-infrared
contributions of the Debye equation in the D + DHO + DHO description of the spectrum [29], see Fig. 4. We therefore use the modified
Debye equation ðDi Þ suggested by Turton and Wynne [30], which
contains the inertial rise constant, clib , in addition to the dielectric
relaxation time, s1 , yielding the Di + DHO + DHO model
e e2
1
1
1
1
þ
ði2
1
þ
i2
p
m
s
Þ
p
m
s
1
1 þ clib s1
1 ð1 þ clib s1 Þ
2
2
ðe2 e3 Þm2
ðe3 e1 Þm3
þ 2
þ
þe
m2 m2 þ imc2 m23 m2 þ imc3 1
^eðmÞ ¼
ð5Þ
In Eq. (5) the static relative permittivity e, as well as e2 ; e3 , and e1
are the limits of the individual dispersion steps to e0 ðmÞ which define
the amplitudes S1 ¼ e e2 ; S2 ¼ e2 e3 , and S3 ¼ e3 e1 of the
three modes. According to Turton and Wynne [30] the inertial rise
constant, clib , is in the order of the average librational frequency
and thus associated with the resonance frequencies of the two
DHO modes of Eq. (5). Trial fits, where clib was varied in the range
of 1.5–2.5 THz, revealed a small but not systematic effect on v2r
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J. Hunger et al. / Chemical Physics Letters 471 (2009) 85–91
a
b
Fig. 2. (a) Dielectric permittivity, e0 , and (b) dielectric loss, e00 , of dichloromethane at temperatures from 278.15 to 308.15 K. Symbols show experimental data, lines represent
the Di þ DHO fit. Arrows indicate increasing temperature.
and negligible cross-correlations of this quantity with the remaining fit parameters. Thus, we fixed the inertial rise constant to
clib ¼ 2 THz in the final fit presented in Table 1. As can be seen from
Figs. 3 and 4 this Di þ DHO þ DHO model provides a very good fit of
the experimental spectrum at 25 °C, albeit with a small low-frequency shift for the calculated maximum ð 71 cm1 Þ of the absorption coefficient, a, relative to the experimental value ( 77 cm1 ;
Fig. 4).
As shown below, the relaxation centred 70 GHz, which dominates the dielectric spectrum, ^eðmÞ (Fig. 3), can be unambiguously
assigned to the rotational diffusion of CH2 Cl2 dipoles. The two
DHO modes resonating at 30 cm1 ð0:893 THzÞ and 71 cm1
(2.13 THz) determine the shoulder and the peak observed for
aðmÞ (Fig. 4). The ratio of the resonance frequencies, m3 =m2 2:4,
compares well with the ratio of libration frequencies expected
from
moments of inertia perpendicular to the dipole vector,
p
ffiffiffiffiffiffiffiffiffithe
ffi
Iy =Ix 3 [8]. In accordance with the simulations of Isegawa
and Kato [14] this suggests that the far-infrared spectrum of
DCM is dominated by librations of the permanent dipoles. However, the simulations also reveal that further spectral contribu-
tions, arising from induced moments and especially crosscorrelations, are far from negligible. Neglect of these broad bands
in our fit model, Eq. (5), may explain the deviations between
experimental and calculated spectrum around 70 cm1 (Fig. 4).
However, due to the limited accuracy of the digitized literature
data [5] forming our experimental basis above 50 cm1 implementation of a more elaborate fit model appeared not to be
expedient.
3.2. Temperature dependence
Based on the above results, we now want to discuss the
temperature dependence of DCM relaxation. Unfortunately, the
spectral range of the THz-TDS in the transmission setup was limited to K 1 THz due to the high absorption of DCM so that the
low-frequency libration (m2 mode of Eq. (5)) is covered up to
its resonance frequency m2 , whereas only the onset of the m3
libration is in the experimental frequency window. Unfortunately, the latter contribution, which cannot be neglected at
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J. Hunger et al. / Chemical Physics Letters 471 (2009) 85–91
Fig. 3. Dielectric permittivity, e0 , and loss, e00 , of dichloromethane at 25 °C: j experimental data of this work; d values obtained by Kramers–Kronig transformation of
literature data [5]. Lines represent fit with the Di þ DHO þ DHO model, shaded areas indicate the contributions of the modified Debye ðDi Þ and the two DHO modes.
Fig. 4. Refractive index, n, and absorption coefficient, a, of dichloromethane at 25 °C: j experimental data of this work; d values obtained by Kramers–Kronig transformation
of literature data [5]. Solid lines represent fit with the modified Di þ DHO þ DHO model, dashed lines the fit with the classical D + DHO + DHO model.
Table 1
Parameters (limiting permittivities, ej , relaxation time, s1 , inertial rise constant, clib , damping constants, cj , resonance frequencies,
Di þ DHO þ DHO model, Eq. (5), fitting ^eðmÞ of dichloromethane at 25 °C in the frequency range 8:5 6 m=GHz 6 4300.
e
8.81
a
s1
clib
ðpsÞ
ðTHzÞ
2.23
2a
Parameter fixed during fitting procedure.
e2
3.89
c2
m2
ðTHzÞ
ðTHzÞ
2.44
0.893
e3
2.56
mj , and reduced error function, v2r ) of the
c3
m3
ðTHzÞ
ðTHzÞ
2.79
2.13
e1
1.98
v2r ¼ 96:4 105 .
1 THz (see Fig. 3), is too far outside the spectral range covered
in the experiment to be properly resolved in the fit. Conse-
quently, its presence slightly biases the fits of the temperaturedependent spectra.
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J. Hunger et al. / Chemical Physics Letters 471 (2009) 85–91
Table 2
Parameters (limiting permittivities, ej , relaxation time, s1 , inertial rise constant, clib ,
damping constant, c2 , resonance frequency, m2 , and reduced error function, v2r ) of the
Di þ DHO model at the investigated temperatures, T.
T
(K)
e
278.15
288.15
298.15
308.15
9.73
9.27
8.83
8.43
a
s1
clib
ðpsÞ
ðTHzÞ
2.74
2.41
2.17
2.03
2a
2a
2a
2a
e2
3.91
3.92
3.77
3.88
c2
m2
ðTHzÞ
ðTHzÞ
1.88
1.94
1.76
1.86
0.89a
0.89a
0.89a
0.89a
e3
v2r 105
2.44
2.43
2.36
2.34
228
242
188
369
Parameter fixed during fit procedure.
Different models have been tested to describe the experimental
data of Fig. 2. It was found that the best fit was achieved with the
Di þ DHO model
^eðmÞ ¼
þ
e e2
1 ð1 þ clib s1 Þ1
ðe2 e3 Þm22
þe
m22 m2 þ imc2 3
1
1
1 þ ði2pms1 Þ 1 þ i2pms1 þ clib s1
ð6Þ
where the resonance frequency of the DHO mode was fixed to the
value obtained at 25 °C, m2 ¼ 0:89 THz. This procedure seems reasonable as in contrast to relaxation processes the location of libration modes depends only weakly on temperature [5].
The obtained parameters are listed in Table 2, Fig. 2 compares
fits and experimental data. The small deviations at m J 100 GHz
can almost certainly be attributed to the small contribution of
the neglected 2 THz resonance (Fig. 3). Nevertheless, comparison
of the 298 K data from Table 2 with results of the full fit (Table
1) reveals that the dielectric parameters e; e2 ; e3 , and s1 obtained
with the Di þ DHO model are only weakly biased by the limitation
of the spectral range to 61 THz (Fig. 5). At all temperatures the
extrapolated static permittivities, e, of this study are in excellent
agreement with data obtained with conventional capacitor methods [1]. Additionally, the value of e1 obtained with the
Di þ DHO þ DHO model at 25 °C (Table 1 and Fig. 5) and the
squared refractive index of Ref. [31] agree within our experimental
a
uncertainty, suggesting that the full intermolecular dynamics of
DCM is practically covered at 25 °C. On the other hand, the static
permittivity and the relaxation time obtained by Vij et al. [8] from
fitting a single Cole–Cole equation to their spectra deviate considerably from our results (Fig. 5). The same is true for the simulated e
and s of Isegawa and Kato [14], probably reflecting the well-known
difficulties encountered in the quantitative computer simulation of
liquid-state dielectric properties [32].
Comparison of s1 with relaxation times from other experimental techniques allows to conclude on the mechanism behind the
observed dielectric relaxation. For rotational diffusion of a molecule it is expected [11] that the molecular correlation times sL of
rank L fulfill the relation
sL ¼
2srot
LðL þ 1Þ
ð7Þ
where srot ð¼ sL¼1 Þ is the rotational correlation time of a probed
intramolecular vector. Correlation times accessible with NMR and
Raman spectroscopy are single-particle relaxation times of rank
L ¼ 2. Dielectric spectroscopy probes L ¼ 1 but the experimentally
accessible relaxation time (s1 of Table 2) is a collective property
[11] which has to be converted to the corresponding rotational correlation time with the Powles–Glarum equation [33,34]
srot ¼
2e þ e1
s1
3e
ð8Þ
The obtained values for srot are displayed in Fig. 6.
For isotropic rotational diffusion srot is independent of the chosen vector, whereas in the case of anisotropic reorientation CH2 Cl2
rotation around the x-axis (Fig. 1) should be different from that
around the y- and z-axes [15]. Thus srot should depend on the
orientation of the monitored vector relative to ðx; y; zÞ, with DS
only monitoring rotations around x and y. If the moments of
Iy Iz , were determining DCM dynamics, then
inertia,
Ix
pffiffiffiffiffiffi
10sx sy sz would be expected. The difference between reorientation around x and the other axes should be less pronounced (of
the order of 1:5sx sy sz ) if viscous friction combined with the
asymmetry in the molecular shape predominates [15].
b
Fig. 5. (a) Limiting permittivities (e: squares, e2 : circles, e3 : triangles, and e1 : diamonds) extracted from DCM spectra with Eqs. (5) and (6), together with the squared
refractive index, n2633 nm ([31], dotted line) and the static permittivity, e (dashed line), determined with low-frequency capacitance measurements [1]. (b) Relaxation time s1
(symbols) and fit with Eq. (10) (line). Open symbols represent parameters obtained at 25 °C with the Di þ DHO þ DHO model from the spectrum covering
8:5 GHz 6 m 6 4:3 THz; filled symbols show the results of the Di þ DHO model applied to the restricted frequency range of 8:5 GHz 6 m K 1 THz. Also included are literature
data from Vij et al. [8] (half filled symbols) and from Isegawa and Kato [14] (open symbols with cross).
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J. Hunger et al. / Chemical Physics Letters 471 (2009) 85–91
Intuitively, one would expect the latter situation for the diffusive reorientation of a molecule in a dense medium. However,
based on the comparison of 13C- and 35Cl NMR data Rodriguez
et al. [15] concluded that DCM reorientation is highly anisotropic
and determined by inertial motion. This may be a reflection of different weights of both librational motions of DCM on the timeintegrated relaxation times determined by 13C- and 35Cl NMR. On
the other hand, it should be noted that the value of srot from 35Cl
NMR is rather sensitive to the choice of the quadrupole coupling
constant required for the analysis of the experimental relaxation
rates. Hacura et al. [16] determined the rotational correlation times
of the vectors associated with three Raman bands as a function of
temperature and pressure. According to this study, and in contrast
to the above NMR results, the observed correlation times for rotation around x, y, and z do not differ within experimental accuracy
at those temperatures relevant to the present study, suggesting
rather isotropic reorientation. The situation becomes even less
clear when the widely scattering correlation times compiled in
Ref. [7] are also considered.
Fig. 6 compares the srot data determined in this investigation
with rotational correlation times from 13C NMR studies [15] and
averaged srot values calculated from the Raman data of Hacura
et al. [16]. Clearly, the agreement between the different techniques
is very good. Since none of the vectors probed by NMR and Raman
coincides with the dipole vector it can be concluded that DCM
reorientation is isotropic in the diffusive regime. This is in line with
the observation that a Debye equation is sufficient to describe the
low-frequency component of ^eðmÞ.
Analysis of the temperature dependence of srot in terms of the
extended Stokes–Einstein–Debye theory (SED) [35]
srot ¼
3V eff g
þ s0rot
kB T
ð9Þ
yields the effective volume of rotation, V eff , required by a CH2 Cl2
molecule. In Eq. (9) kB is the Boltzmann constant and T the thermodynamic temperature. V eff ¼ fCV m , is determined by the molecular
volume, V m , and the shape factor, f, of the particle [36]. Additionally,
a hydrodynamic friction coefficient, C, appears which is generally
treated as an empirical parameter but its limiting values for stick
ðC stick ¼ 1Þ and slip ðC slip ¼ 1 f 2=3 Þ boundary conditions are
known. The empirical axis intercept, s0rot , is occasionally interpreted
as the correlation time of the freely rotating particle.
The viscosities, g, required for the SED analysis of the rotational
correlation times of this investigation were taken from the literature [1]. Assuming slip boundary conditions ðC slip ¼ 0:129Þ a
weighted fit of srot vs. 1=T yields the molecular volume of
3
V m ¼ ð25 1Þ Å from the slope, whereas 59 Å3 was estimated by
approximating the DCM molecule as a prolate ellipsoid with principal axes of lengths a ¼ 6:52 Å and b ¼ c ¼ 4:16 Å ðf ¼ 1:230;
from van der Waals radii [37] of the atoms). This difference, yielding C ¼ 0:06, may point at sub-slip friction for DCM reorientation.
However, it should be kept in mind that a prolate ellipsoid is certainly only a rough approximation for CH2 Cl2 . Similar caution applies for the obtained axis intercept, s0rot ¼ ð0:59 0:01Þ ps.
Although comparable to the free-rotor correlation time [38] for
rotation around the y-axis (0.3 ps) discussion of this quantity is
not appropriate.
Further insight into the mechanism of DCM relaxation is provided by its Eyring [39] activation enthalpy, DH– , and entropy,
DS– , which can be derived from the temperature dependence of s1
h
DS–
DH –
þ
lnðT s1 Þ ¼ ln
kB
R
RT
ð10Þ
In Eq. (10) h and R are the Planck and the gas constant, respectively.
From the s1 data of Table 2 the activation enthalpy of
1
DH– ¼ ð4:8 0:5Þ kJ mol
and the activation entropy of
1
DS– ¼ ð5:8 1:8Þ J K1 mol were obtained (Fig. 5b). These values are comparable to the activation parameters of acetonitrile
1
1
[40]),
(DH– ¼ ð4:6 0:2Þ kJ mol ; DS– ¼ ð9:8 0:6Þ J K1 mol
which is also regarded as a simple dipolar liquid. The significantly
smaller value of jDS– j for DCM suggests that compared to acetonitrile smaller structural changes of the environment are required
for the reorientation of a CH2 Cl2 molecule, meaning that DCM
dynamics are less cooperative.
Under the assumption that the fast dipole moment fluctuations
associated with the librations do not correlate with the slower
rotational diffusion, the effective dipole moment, leff , of the DCM
molecules in the liquid can be obtained from the relaxation amplitude, S1 , with the Cavell equation [41]
2e þ 1
e
S1 ¼
NA c
l2
kB T e0 eff
ð11Þ
where NA is the Avogadro constant, e0 the vacuum permittivity and
c is the molar concentration of DCM, calculated from the density
data of Ref. [1]. Averaging over all investigated temperatures the
data of Table 2 yield the effective dipole moment of
leff ¼ ð1:93 0:04Þ D for CH2 Cl2 .
leff relates to the dipole moment of the isolated molecule, l, via
pffiffiffi
leff ¼ g lap ¼
pffiffiffi
gl
1 fr a
ð12Þ
3
where a ¼ 6:82 Å [3] is the molecular polarizability and fr the reaction field factor [42] of DCM. The Kirkwood factor g ¼ l2eff =l2ap is a
measure for orientational correlations among the dipoles in the liquid [42].
Under the assumption of a spherical reaction field of radius
a=2 ¼ 3:26 Å for DCM insertion of l ¼ 1:61 D [3] into Eq. (12)
yields the value of lap ¼ 1:93 D, thus g ¼ 1. The virtual identity
of the experimental leff and the calculated lap is certainly accidental.1 Nevertheless, this finding indicates negligible orientational correlations among neighboring dipoles, a result which is in line with
the inference from s1 that DCM relaxation can be viewed as essentially isotropic rotational diffusion of individual dipoles. This is also
supported by a comparison of g with the Kirkwood correlation
Fig. 6. Rotational correlation times, srot , from dielectric spectroscopy (j, this
study), 13C NMR ( , Ref. [15]) and Raman spectroscopy (M, Ref. [16]). Line
represents the fit of the DS data with Eq. (9).
1
Insertion of ðe e1 Þ instead of S1 , i.e. assumption that dipole fluctuations
associated with librations and rotational diffusion are correlated, yields g 1:3.
J. Hunger et al. / Chemical Physics Letters 471 (2009) 85–91
factors given by Richardi et al. [43]: g K ¼ 1:07 from experimental
static permittivity data and g K ¼ 1:15 calculated with statistical
mechanics (note the slightly different assumptions behind the
Kirkwood–Fröhlich [42] and the Cavell [41] equations).
4. Conclusions
[6]
[7]
[8]
[9]
[10]
[11]
[12]
The dielectric properties of dichloromethane over a wide frequency range have been investigated. Data analysis reveals three
contributions to ^eðmÞ, a relaxation at 70 GHz modeled by a modified Debye equation accounting for inertial rise, and two fast
modes at 0:4 THz and 1:8 THz described by damped harmonic
oscillators with resonance frequencies of m2 ¼ 0:89 THz and
m3 ¼ 2:1 THz. The relaxation at low frequencies can be assigned
to rotational diffusion of the dipolar DCM molecules. The data suggest that the diffusive reorientation of the dipole vectors is isotropic. There are no indications for orientational correlations among
the CH2 Cl2 molecules. The two fast modes in the THz region are
dominated by the libration of the permanent CH2 Cl2 dipoles
around the x- and y-axes of the molecule (Fig. 1), albeit some contributions from induced moments and dipole-induced dipole
cross-correlations are likely.
Acknowledgements
The authors thank Prof. W. Kunz (Regensburg) and Prof. H.
Helm (Freiburg) for the provision of laboratory facilities and Dr.
D.A. Turton and Prof. K. Wynne for helpful discussion about fitting
models.
References
[1] D.R. Lide (Ed.), CRC-Handbook of Chemistry and Physics, 85th edn., CRC-Press,
Boca Raton, 2004.
[2] S.S. Chadwick, Ullmann’s Encyclopedia of Industrial Chemistry, Wiley–VCH,
Weinheim, 2006.
[3] M.W. Evans, G.J. Evans, W.T. Coffey, P. Grigolini, Molecular Dynamics, Wiley,
New York, 1982.
[4] M.W. Evans, J. Yarwood, Adv. Mol. Relax. Interact. Process. 21 (1981) 1.
[5] J.K. Vij, C.J. Reid, G.J. Evans, M. Ferrario, M.W. Evans, Adv. Mol. Relax. Interact.
Process. 22 (1982) 79.
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
91
J.K. Vij, Y.P. Kalmykov, J. Chem. Phys. 99 (1993) 2506.
M.W. Evans, M. Ferrario, Adv. Mol. Relax. Interact. Process. 23 (1982) 113.
J.K. Vij, F. Hufnagel, T. Grochulski, J. Mol. Liq. 49 (1991) 1.
Z. Kisiel, K. Leibler, A. Gerschel, J. Phys. E: Instrum. 17 (1984) 240.
D. Bertolini, M. Cassettari, G. Salvetti, T.E.S. Veronesi, Rev. Sci. Instrum. 12
(1990) 61.
C.F.J. Böttcher, P. Bordewijk, Theory of Electric Polarization, vol. 2, Elsevier,
Amsterdam, 1978.
F. Kremer, A. Schönhals (Eds.), Broadband Dielectric Spectroscopy, Springer,
Berlin, 2003.
H. Torii, J. Mol. Liq. 119 (2005) 31.
M. Isegawa, S. Kato, J. Chem. Phys. 127 (2007) 244502.
A.A. Rodriguez, S.J.H. Chen, M. Schwartz, J. Magn. Reson. 74 (1987) 114.
A. Hacura, T.W. Zerda, M. Kaczmarski, J. Raman Spectrosc. 11 (1981) 427.
B. Gestblom, I. Svorstøl, J. Songstad, J. Phys. Chem. 90 (1986) 4684.
V.P. Pawar, S.C. Mehrotra, J. Mol. Liq. 108 (2003) 95.
S. Schrödle, G. Annat, D.R. MacFarlane, M. Forsyth, R. Buchner, G. Hefter, Chem.
Commun. (2006) 1748.
J. Hunger, A. Stoppa, R. Buchner, G. Hefter, J. Phys. Chem. B 112 (2008) 12913.
S. Schrödle, R. Buchner, W. Kunz, J. Phys. Chem. B 108 (2004) 6281.
J. Barthel, K. Bachhuber, R. Buchner, H. Hetzenauer, M. Kleebauer, Ber. BunsenGes. Phys. Chem. 95 (1991) 853.
P. Uhd Jepsen, B.M. Fischer, A. Thoman, H. Helm, J.Y. Suh, R. Lopez, R.F.
Haglund, Phys. Rev. B 74 (2006) 205103.
B.M. Fischer, Ph.D. Dissertation, Freiburg, Germany, 2005.
J.E. Bertie, S.L. Zhang, C.D. Keefe, Vib. Spectr. 8 (1995) 215.
J.R. Birch, T.J. Parker, in: K.J. Button (Ed.), Infrared and Millimeter Waves, vol. 2,
Academic Press, New York, 1979.
R. Buchner, T. Chen, G. Hefter, J. Phys. Chem. B 108 (2004) 2365.
A. Stoppa, J. Hunger, R. Buchner, G. Hefter, A. Thoman, H. Helm, J. Phys. Chem. B
112 (2008) 4854.
S. Havriliak, S.J. Havriliak, Dielectric and Mechanical Relaxation in Materials,
Hanser, New York, 1997.
D.A. Turton, K. Wynne, J. Chem. Phys. 128 (2008) 154516.
S. Valkai, J. Liszi, I. Szalai, J. Chem. Thermodynam. 30 (1998) 825.
C. Schröder, J. Hunger, A. Stoppa, R. Buchner, O. Steinhauser, J. Chem. Phys. 129
(2008) 184501.
J.G. Powles, J. Chem. Phys. 21 (1953) 633.
S.H. Glarum, J. Chem. Phys. 33 (1960) 639.
J.C. Dote, D. Kivelson, R.N. Schwartz, J. Chem. Phys. 85 (1981) 2169.
J.C. Dote, D. Kivelson, J. Phys. Chem. 87 (1983) 3889.
K. Tanabe, Spectrochim. Acta 32 (1976) 1129.
F.J. Bartoli, T.A. Litovitz, J. Chem. Phys. 56 (1972) 413.
S. Glasstone, K.J. Laidler, H. Eyring, The Theory of Rate Processes, McGraw-Hill,
New York, 1941.
A. Stoppa, S. Schrödle, G. Hefter, R. Buchner, unpublished results.
E.A.S. Cavell, P.C. Knight, M.A. Sheikh, Trans. Faraday Soc. 67 (1971) 2225.
C.F.J. Böttcher, Theory of Electric Polarization, vol. 1, Elsevier, Amsterdam,
1973.
J. Richardi, P.H. Fries, H. Krienke, J. Phys. Chem. B 102 (1998) 5196.